Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [proof-writing]

For questions about the formulation of a proof. This tag should not be the only tag for a question and should not be used to ask for a proof of a statement.

Questions with this tag are about the presentation of a mathematical proof. Questions might include:

  • Should I include [x-mathematical detail] at [y-part of this proof]?
  • Is the following a sufficient proof of [x-mathematical tidbit]?
  • I have written the following proof, could I somehow improve it, does it have good flow/can I improve readability?

But this tag is not for asking someone else to write a proof for you, or for how to answer some question. Questions such as: My professor asked me to prove the Pythagorean theorem and I don't know how to begin are not to have this tag.

This tag is intended for use along with other, more "mathematical" tags. A question about the writing of a proof in abstract algebra, for example, should have as well. This tag can be used along with the proof verification tag.

See here for a useful set of guidelines for writing a solution.

15776 questions
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Show that the field Q[sqrt2] cannot be ordered using the defined relation

The complete questions states: On $\mathbb Q\:$[$\sqrt2 $] we define the relation: $\mathbb a+b\sqrt2 < a'+b'\sqrt2$ if $\mathbb a
user133678
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Question with this proof

The integer $m$ is odd if and only if there exists q $\in \mathbb{Z}$ such that $m=2q+1$ I know that $m$ is even if 2|n, and $n$ is odd if $n$ is not even. I also know the division algorithm, which is that for every $m$ there exists $m = qn + r$.
user135340
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Is there a simple way to prove the Four Colour Theorem?

The four colour theorem says that: Given any separation of a plane into contiguous regions, producing a figure called a map, no more than four colours are required to colour the map so that no two adjacent regions have the same colour. From…
Anonymous Computer
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Basic proof problem from "How to Prove it A Structured Approach"

I got the book How to Prove it A Structured Approach and I'm ashamed to admit I failed to even do the first problem in the introduction chapter: a) Factor $2^{15} - 1 = 32767$ into a product of two smaller positive integers. b) Find an integer $x$…
darkradeon
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If $a\lt 0$ and $b\lt 0,$ then $ab\gt0$.

$\quad$The following assertion is somewhat less obvious: If $a\lt 0$ and $b\lt 0,$ then $ab\gt0$. The only difficulty presented by the proof is unraveling of definitions. The symbol $a\lt 0$ means, by definition, $0\gt a$, which means $0-a=-a$ in…
user108343
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Proof of proportions in proportion by composition and decomposition?

What is the proof that $\frac{a+b}{a-b}=\frac{c+d}{c-d}$ given that $\frac{a}{b}=\frac{c}{d}$ Here's what I've got so far: $$\begin{array}{l} \text{Statements} &&&&&&&&&&&&&&&& \text{Reasons} \\\\ \ \text{1.} \frac{a}{b}=\frac{c}{d} …
Daniel
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How would I go about proving this?

Question is: Let $n$ represent a positive integer. Describe the largest set of values $n$ for which you think that $2^n < n!$ I'm not sure I get this question. For $n > 3$, it seems like $2^n$ is always less than $n!$ So how would I prove this…
muros
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Prove that if f is increasing on an interval I, then f is one to one on I.

How do I even begin to do this problem? I don't know where to even begin. The professor of the class tried to give us hints (as this is a redo to our homework) and said "The contrapositive is 'If f is not one to one, then f is not increasing.'…
DChung91
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Using contrapositive how to prove $x,y \in \mathbb R \wedge x \lt 0 \implies \nexists y$ such that $x=y^2$?

Consider the following implication, $x,y \in \mathbb R \wedge x \lt 0 \implies \nexists y$ such that $x=y^2$. Question asks to use contrapositive, so here is my proof: Let $x=y^2$ (since it's negation of conclusion). I want to show that $x \ge…
user_1357
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How do I prove by induction?

For example if i wanted to prove: $1^2 + \dots + n^2 = \frac {n(n + 1)(2n + 1)} {6}$ by induction. I'm not sure where to start. Thanks.
Kat
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Prove using the Intermediate Value Theorem that $ f(x) = e^x $ and $ g(x) = x^e $ intersect.

Problem: Prove using the Intermediate Value Theorem that $ f(x) = e^x $ and $ g(x) = x^e $ intersect. My attempt: First, here is the definition of the IVT that I am familiar with - "Suppose $f$ is continuous over $[a,b]$ and $f(a) \neq f(b)$. If $Y$…
kai
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Can we use Prove by Contradiction to prove a statement FALSE?

Proof by contradiction proves a statement by proving that the statement cannot be untrue. If a statement is FALSE, can we still use proof by contradiction? For example, here is a statement: Let $m$ and $n$ be inegers. If $2m+n$ is even, then $m$ and…
Ludwig Gershwin
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Can we give an algorithm to prove a statement?

Can we prove a statement by providing an algorithm that is true for all conditions of the statement? Or do we need to prove the validity of the algorithm too? As an example, suppose we need to prove that each number $n$ can be written as $2^km$ for…
Gerard
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Induction proof with matrix multiplication

I am working on the following exercise from Prof. Richard Earl (Oxford). I completed the first part, which was quite straightforward. However, I don't know how to move to the second one. I believe the second portion of the exercise requires the…
bru1987
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Is cartesian product of two sets a subset of power set of power set of their union?

Let X,Y be two sets. Is this true that "$X\times Y$ is subset of $P(P(X\cup Y)$"? I tried to solve like this: If we choose an element of $X\times Y$, then it should be an element of $P(P(X\cup Y)$. Let this element be A. Assume A is an element of…
emre
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